Systems and methods for locating a signal source

ABSTRACT

A method of estimating the location of a signal source comprises, by a processing unit:
         determining ΔΔφ m,n  which represents a difference between accumulated phases of signals, S m  and S n , received by at least one pair of the receivers,   determining a first estimate of the location of said signal source based on position data and ΔΔφ m,n  of said at least one pair of receivers, said first estimate being associated with an accuracy area,   determining data representative of difference in times of arrival of modulation patterns of the signals S m , S n , wherein said data comprise an ambiguity, and   for said at least one pair of receivers, using at least said data representative of difference in times of arrival of the modulation patterns of the signals, ΔΔφ m,n , and said accuracy area, to obtain second estimates ê Src   k  of the source location, at least some of them being located within the accuracy area

TECHNOLOGICAL FIELD

The invention is in the field of signal processing and relates to techniques for locating a source of a signal by a plurality of receivers.

BACKGROUND

Various techniques are known in the art for determining the location of a signal source by receiving and processing the signal emitted from the source by a plurality of signal receivers.

There is now a need to provide improved methods and systems for locating a signal source.

GENERAL DESCRIPTION

In accordance with certain aspects of the presently disclosed subject matter, there is provided a method of estimating the location of a signal source, the method comprising:

providing measured data indicative of a signal S_(n) received from a signal source by each of a number of at least two receivers {Rc_(n)} during time intervals {Δt_(n)}, where n is an index indicating the n^(th) receiver Rc_(n), and providing position data indicative of positions {R_(n)} of said at least two receivers during said time intervals {Δt_(n)} respectively;

applying a processing to determine differential phase differences ΔΔφ^(m,n) which represent a difference between accumulated phases, Δφ^(m) and Δφ^(n), of the signals, S_(m) and S_(n), received by at least one pair {m,n} of the receivers, Rc_(m) and Rc_(n) during time intervals {Δt_(n)}, {Δt_(m)}, respectively;

applying a processing to determine a first estimate of the location of said signal source based on said position data and said differential phase differences {ΔΔφ^(m,n)} of said at least one pair {m,n} of receivers, said first estimate being associated with an accuracy area;

applying a processing to determine data representative of difference in times of arrival of modulation patterns of the signals S_(m), S_(n) received by said at least one pair {m,n} of receivers, wherein said data comprise an ambiguity; and

for said at least one pair {m,n} of receivers, using at least said data representative of difference in times of arrival of the modulation patterns of the signals, said differential phase differences ΔΔφ^(m,n), and said accuracy area, to obtain one or more second estimates ê_(Src) ^(k) of the source location, wherein at least some of these one or more second estimates ê_(Src) ^(k) of the source location are located within the accuracy area.

In addition to the above features, the method according to this aspect of the presently disclosed subject matter can optionally comprise one or more of features (i) to (xii) below, in any technically possible combination or permutation:

-   -   i. the method comprises using at least said accuracy area to         obtain a limited set of values for said ambiguity;     -   ii. the method comprises solving equations relating differential         phase differences ΔΔφ^(m,n) to the position data of said at         least one pair {m,n} of receivers and to the source location,         and equations relating difference in times of arrival of         modulation patterns of the signals S_(m), S_(n) to the position         data of the receivers and to the source location, for one or         more values of the ambiguity within said limited set, and         providing said one or more second estimates ê_(Src) ^(k) of the         source location based on said solving;     -   iii. the method comprises using the first estimate of the source         location to obtain an estimate of the difference in times of         arrival of the modulation patterns of the signals, and using         said estimate of the difference in times of arrival of the         modulation patterns of the signals, said limited set of values         of said ambiguity and said differential phase differences         ΔΔφ^(m,n) to provide said one or more second estimates ê_(Src)         ^(k) of the source location;     -   iv. the method comprises using the first estimate ê_(Src) ^(k)         of the source location to provide Δ{circumflex over (t)}^(m,n),         wherein Δ{circumflex over (t)}^(m,n) is an estimate of data         representative of difference in times of arrival of the         modulation patterns of the signals;     -   v. the method comprises solving equations relating differential         phase differences ΔΔφ^(m,n) to the position data of the         receivers and to the source location, and equations relating         Δ{circumflex over (t)}^(m,n)+k.PRI to the position data of the         receivers and to the source location, and providing said one or         more second estimates ê_(Src) ^(k) of the source location,         wherein k is an integer selected such that said one or more         second estimates ê_(Src) ^(k) are within said accuracy area;     -   vi. the method comprises obtaining a set of limited values for         said ambiguity, said obtaining comprising selecting a plurality         of multiples of a pulse repetition interval of the signals         S_(m), S_(n), for which associated data representative of         difference in times of arrival of modulation patterns of the         signals provide an estimate of the location of the source which         is within the accuracy area;     -   vii. the method comprises selecting an optimized set of values         of said ambiguity according to an optimization criterion, said         optimization criterion being representative of at least one of         an error of a solution to equations relating differential phase         differences ΔΔφ^(m,n) to the position data of the receivers and         to the source location, and an error of a solution to equations         relating difference in times of arrival of modulation patterns         of the signals S_(m), S_(n) to the position data of the         receivers and to the source location, and providing said one or         more second estimates ê_(Src) ^(k) of the source location based         on said optimized set of values;     -   viii. each of said signals S_(n) has a constant pulse repetition         interval (PRI), and ∥e−S_(m)∥−∥e−s_(n)∥>PRI.c, wherein e is the         location of the source, s_(m), is the position of the receiver         Rc_(m) and s_(r), is the position of the receiver Rc_(n);     -   ix. signal S_(n) has a PRF which is higher or equal to 100 KHz;     -   x. the method comprises providing measured data indicative of a         signal S_(n) received from a signal source by each of a number         of at least two receivers {Rc_(n)} during a time interval Δt_(i)         of a dwell i, where n is an index indicating the n^(th) receiver         Rc_(n), and providing position data indicative of positions         {R_(n)} of said at least two receivers during said time interval         Δt_(i); applying a processing to determine differential phase         differences ΔΔφ_(i) ^(m,n) which represent a difference between         accumulated phases, Δφ_(i) ^(m) and Δφ_(i) ^(n), of the signals,         S_(m) and S_(n), received by at least one pair {m,n} of the         receivers, Rc_(m) and Rc_(n) during time interval Δt_(i)         applying a processing to determine a first estimate of the         location of said signal source based on position data and said         differential phase differences ΔΔφ_(i) ^(m,n) of said at least         one pair {m,n} of receivers, said first estimate being         associated with an accuracy area, applying a processing to         determine data representative of difference in times of arrival         of modulation patterns of the signals S_(m), S_(n) received by         said at least one pair {m,n} of receivers within said dwell,         wherein said data comprise an ambiguity; for said at least one         pair {m,n} of receivers, and for a plurality of said dwells,         using at least said data representative of difference in times         of arrival of the modulation patterns of the signals, said         differential phase differences ΔΔφ_(i) ^(m,n) and said accuracy         area to obtain one or more second estimates ê_(Src) ^(k) of the         source location, wherein at least some of these one or more         second estimates ê_(Src) ^(k) of the source location are located         within the accuracy area;     -   xi. each signal S_(n) comprises a plurality of modulation         patterns p_(j,i) ^((n)) within dwell i, where n is an index         indicating the n^(th) receiver Rc_(n), and j an index         representing the j^(th) modulation pattern, wherein said         computing of ΔΔφ_(i) ^(m,n) comprises computing Δφ_(pj,i) ^(m,n)         which is representative of the phase difference between the         phase of modulation pattern p_(j,i) ^((n)) received at receiver         Rc_(n) and the phase of modulation pattern p_(j,i) ^((m))         received at receiver Rc_(n), the method comprising using a bound         value which bounds the value of the difference between Δφ_(pj,i)         ^(m,n) for two consecutive modulation patterns, to limit a phase         ambiguity present in Δφ_(pj,i) ^(m,n);     -   xii. a dimension of the accuracy area has a length L, wherein         said ambiguity is modelled as k.PRI, wherein PRI is the pulse         repetition interval of signal Sn, and k is selected within a         range which is between K1 and K2, wherein:

$K_{1} = {{\frac{\frac{- L}{2}}{{PRIC}.c}\mspace{14mu}{and}\mspace{14mu} K_{2}} = {\frac{\frac{+ L}{2}}{{PRI}.c}.}}$

According to another aspect of the presently disclosed subject matter there is provided a non-transitory storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform the above mentioned method. In addition, according to some embodiments, there is provided a non-transitory storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform the above mentioned method which comprises one or more of features (i) to (xii).

According to another aspect of the presently disclosed subject matter there is provided a system for locating a signal source emitting a signal S, the system comprising one or more processing units configured to:

provide measured data indicative of a signal S_(n) received from a signal source by each of a number of at least two receivers {Rc_(n)} during time intervals {Δt_(n)}, where n is an index indicating the n^(th) receiver Rc_(n), and providing position data indicative of positions {R_(n)} of said at least two receivers during said time intervals {Δt_(n)} respectively;

apply a processing to determine differential phase differences ΔΔφ^(m,n) which represent a difference between accumulated phases, Δφ^(m) and Δφ^(n), of the signals, S_(m) and S_(n), received by at least one pair {m,n} of the receivers, Rc_(m) and Rc_(n) during time intervals {Δt_(n)}, {Δt_(m)}, respectively;

apply a processing to determine a first estimate of the location of said signal source based on said position data and said differential phase differences {ΔΔφ^(m,n)} of said at least one pair {m,n} of receivers, said first estimate being associated with an accuracy area;

apply a processing to determine data representative of difference in times of arrival of modulation patterns of the signals S_(m), S_(n) received by said at least one pair {m,n} of receivers, wherein said data comprise an ambiguity, and

for said at least one pair {m,n} of receivers, use at least said data representative of difference in times of arrival of the modulation patterns of the signals, said differential phase differences ΔΔφ^(m,n), and said accuracy area to obtain one or more second estimates ê_(Src) ^(k) of the source location, wherein at least some of these one or more second estimates ê_(Src) ^(k) of the source location are located within the accuracy area.

In addition to the above features, the system according to this aspect of the presently disclosed subject matter can optionally comprise one or more of features (xii) to (xxiv) below, in any technically possible combination or permutation:

-   -   xiii. the system is configured to use at least said accuracy         area to obtain a limited set of values for said ambiguity;     -   xiv. the system is configured to solve equations relating         differential phase differences ΔΔφ^(m,n) to the position data of         said at least one pair {m,n} of receivers and to the source         location, and equations relating difference in times of arrival         of modulation patterns of the signals S_(m), S_(n) to the         position data of the receivers and to the source location, for         one or more values of the ambiguity within said limited set, and         provide said one or more second estimates ê_(Src) ^(k) of the         source location based on said solving;     -   xv. the system is configured to use the first estimate of the         source location to obtain an estimate of the difference in times         of arrival of the modulation patterns of the signals, and use         said estimate of the difference in times of arrival of the         modulation patterns of the signals, said limited set of values         of said ambiguity and said differential phase differences         ΔΔφ^(m,n) to provide said one or more second estimates ê_(Src)         ^(k) of the source location;     -   xvi. the system is configured to use the first estimate ê_(S)         _(rc) of the source location to provide Δ{circumflex over         (t)}^(m,n), wherein Δ{circumflex over (t)}^(m,n) is an estimate         of data representative of difference in times of arrival of the         modulation patterns of the signals;     -   xvii. the system is configured to solve equations relating         differential phase differences ΔΔφ^(m,n) to the position data of         the receivers and to the source location, and equations relating         Δ{circumflex over (t)}^(m,n)+k.PRI to the position data of the         receivers and to the source location, and provide said one or         more second estimates ê_(Src) ^(k) of the source location,         wherein k is an integer selected such that said one or more         second estimates ê_(Src) ^(k) are within said accuracy area;     -   xviii. the system is configured to obtain a set of limited         values for said ambiguity, said obtaining comprising selecting a         plurality of multiples of a pulse repetition interval of the         signals S_(m), S_(n), for which associated data representative         of difference in times of arrival of modulation patterns of the         signals provide an estimate of the location of the source which         is within the accuracy area;     -   xix. the system is configured to select an optimized set of         values of said ambiguity according to an optimization criterion,         said optimization criterion being representative of at least one         of an error of a solution to equations relating differential         phase differences ΔΔφ^(m,n) to the position data of the         receivers and to the source location, and an error of a solution         to equations relating difference in times of arrival of         modulation patterns of the signals S_(m), S_(n) to the position         data of the receivers and to the source location, and provide         said one or more second estimates ê_(Src) ^(k) of the source         location based on said optimized set of values;     -   xx. each of said signals S_(n) has a constant pulse repetition         interval (PRI), and ∥e−s_(m)∥−∥e−s₂∥>PRI.c, wherein e is the         location of the source, s_(m), is the position of the receiver         Rc_(m) and s_(r), is the position of the receiver Rc_(n);     -   xxi. signal S_(n) has a PRF which is higher or equal to 100 KHz;     -   xxii. the system is configured to provide measured data         indicative of a signal S_(n) received from a signal source by         each of a number of at least two receivers {Rc_(n)} during a         time interval Δt_(i) of a dwell i, where n is an index         indicating the n^(th) receiver Rc_(n), and provide position data         indicative of positions {R_(n)} of said at least two receivers         during said time interval Δt_(i) apply a processing to determine         differential phase differences ΔΔφ^(m,n) which represents a         difference between accumulated phases, Δφ_(i) ^(m) and Δφ_(i)         ^(n), of the signals, S_(m) and S_(n), received by at least one         pair {m,n} of the receivers, Rc_(m) and Rc_(n) during time         interval Δt_(i); apply a processing to determine a first         estimate of the location of said signal source based on position         data and said differential phase differences ΔΔφ_(i) ^(m,n) of         said at least one pair {m,n} of receivers, said first estimate         being associated with an accuracy area; apply a processing to         determine data representative of difference in times of arrival         of modulation patterns of the signals S_(m), S_(n) received by         said at least one pair {m,n} of receivers within said dwell,         wherein said data comprise an ambiguity; for said at least one         pair {m,n} of receivers, and for a plurality of said dwells,         using at least said data representative of difference in times         of arrival of the modulation patterns of the signals, said         differential phase differences ΔΔφ^(m,n), and said accuracy area         to obtain one or more second estimates ê_(Src) ^(k) of the         source location, wherein at least some of these one or more         second estimates ê_(Src) ^(k) of the source location are located         within the accuracy area;     -   xxiii. each signal S_(n) comprises a plurality of modulation         patterns p_(j,i) ^((n)) within dwell i, where n is an index         indicating the n^(th) receiver Rc_(n), and j an index         representing the j^(th) modulation pattern, wherein said         computing of ΔΔφ_(i) ^(m,n) comprises computing Δφ_(pj,i) ^(m,n)         which is representative of the phase difference between the         phase of modulation pattern p_(j,i) ^((n)) received at receiver         Rc_(n) and the phase of modulation pattern p_(j,i) ^((m))         received at receiver Rc_(m), wherein the system is configured to         use a bound value which bounds the value of the difference         between Δφ_(pj,i) ^(m,n) for two consecutive modulation         patterns, to limit a phase ambiguity present in Δφ_(pj,i)         ^(m,n);     -   xxiv. a dimension of the accuracy area has a length L, said         ambiguity is modelled as k. PRI, with PRI the pulse repetition         interval of signal S_(n), and k is selected within a range which         is between K₁ and K₂, wherein:

$K_{1} = {{\frac{\frac{- L}{2}}{{PRIC}.c}\mspace{14mu}{and}\mspace{14mu} K_{2}} = \frac{\frac{+ L}{2}}{{PRI}.c}}$

According to some embodiments, the proposed solution is able to determine the location of a source which emits a signal with a high PRF (pulse repetition frequency).

According to some embodiments, the proposed solution is able to determine the location of a source which emits a signal with a constant PRI (pulse repetition interval). According to some embodiments, the proposed solution is able to determine the location of a source with signal receivers which are located “far” (definitions will be provided hereinafter in the specification) from each other relative to the source (and in particular at a distance which creates an ambiguity between the modulation patterns received at each signal receiver which needs to be reduced or solved for estimating the source location, this ambiguity being a multiple of the PRI).

According to some embodiments, the proposed solution is able to reduce an ambiguity present in the DTOA method (difference time of arrival).

According to some embodiments, the proposed solution provides an estimation of the source location which is more precise and more reliable.

According to some embodiments, the proposed solution provides rapidly an estimation of the source location which improves in time.

According to some embodiments, the proposed solution relies on the calculation of accumulated phases of the signals received at each receiver, wherein this calculation can be performed at each signal receiver. This provides a reduction of the data communication bandwidths and/or of the time required to transmit the data.

According to some embodiments, the proposed solution relies on various techniques to reduce the ambiguity which can arise in a method relying on differential phase measurements and/or in a method relying on DTOA.

According to some embodiments, the proposed solution obviates a need to monitor the trajectories of the signal receivers and their velocities along the trajectory, as would be required by techniques such as FDOA, since only data indicative of the positions of the receivers at two time points (e.g. at the beginning and the end of the time interval during which the phase is accumulated) is required to determine the location of the signal source (in addition to data representative of the signals received at each signal receiver).

BRIEF DESCRIPTION OF THE DRAWINGS

In order to better understand the subject matter that is disclosed herein and to exemplify how it may be carried out in practice, embodiments will now be described, by way of non-limiting example only, with reference to the accompanying drawings, in which:

FIGS. 1A to 1C are schematic illustrations exemplifying embodiments of systems and methods of locating a signal source; wherein FIG. 1A is a flow chart of an embodiment of a method for locating the signal source; FIG. 1B is a non-limitative graphical example of the method of FIG. 1A, and FIG. 1C is a block diagram of an embodiment of a system for locating the signal source;

FIG. 1D is representative of a first estimate of the source location, associated with an accuracy area, using “ddphase” (differential phase differences) equations;

FIG. 1E is representative of additional possible estimates of the source location which match the accuracy area, associated with various possible values of an ambiguity;

FIG. 2 is representative of an embodiment of a method of determining data representative of the differential times of arrival of modulation patterns for at least one pair of receivers;

FIG. 3 is representative of an embodiment of a method of determining possible estimates of the source location;

FIG. 4 is representative of an embodiment of a method of determining differential phase differences between accumulated phases of signals received by at least one pair of receivers;

FIGS. 5 and 6 describe possible methods of reducing an ambiguity present in the accumulated phases and/or in the differential phase differences between the accumulated phases; and

FIGS. 7A and 7B illustrate possible embodiments of methods of determining the phases and unwrapping the phases of modulation patterns received at each receiver.

DETAILED DESCRIPTION OF EMBODIMENTS

In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be understood by those skilled in the art that the presently disclosed subject matter may be practiced without these specific details. In other instances, well-known methods have not been described in detail so as not to obscure the presently disclosed subject matter.

Unless specifically stated otherwise, as apparent from the following discussions, it is appreciated that throughout the specification discussions utilizing terms such as “processing”, “applying”, “determining”, “using”, “solving”, “estimating”, “reducing”, “obtaining”, “selecting”, “computing” or the like, refer to the action(s) and/or process(es) of a processing unit that manipulates and/or transforms data into other data, said data represented as physical, such as electronic, quantities and/or said data representing the physical objects.

The term “processing unit” as disclosed herein should be broadly construed to include any kind of electronic device with data processing circuitry, which includes for example a computer processing device operatively connected to a computer memory (e.g. digital signal processor (DSP), a microcontroller, a field programmable gate array (FPGA), and an application specific integrated circuit (ASIC), etc.) capable of executing various data processing operations.

It can encompass a single processor or multiple processors, which may be located in the same geographical zone or may, at least partially, be located in different zones and may be able to communicate together.

The term “non-transitory memory” as used herein should be expansively construed to cover any volatile or non-volatile computer memory suitable to the presently disclosed subject matter.

Embodiments of the presently disclosed subject matter are not described with reference to any particular programming language. It will be appreciated that a variety of programming languages may be used to implement the teachings of the presently disclosed subject matter as described herein.

The invention contemplates a computer program being readable by a computer for executing one or more methods of the invention. The invention further contemplates a machine-readable memory tangibly embodying a program of instructions executable by the machine for executing one or more methods of the invention.

Reference is made together to FIGS. 1A, 1B and 1C exemplifying possible embodiments for locating a signal source Src.

FIG. 1A is a flow chart of a method 100 of locating the signal source Src according to some embodiments of the present invention. FIG. 1B is a schematic illustration of the operation of several receivers Rc₁-Rc_(n) for locating the signal source Src according to the method depicted in FIG. 1A, and FIG. 1C is a block diagram of a system 200 configured according to certain embodiments for carrying out one or more methods described hereinafter (for example, carrying out the operations of method 100) for locating the signal source Src.

It should be noted that the operations 105-170 may be performed in a centralized manner (e.g. in a central processing utility) or, according to some embodiments, certain of these operations, such as operation 110 and/or operation 120, may be performed by one or more processing units associated with (e.g. integrated-/connected- with and/or adjacent to) respective ones of the receivers Rc₁-Rc_(n) while other operations such as 130-170 which concern data about the signals from several receivers, may be centralized and performed by a central processing utility (which comprises one or more processing units) and/or distributed among several such utilities. The latter case provides for reducing the amount of information that needs to be transmitted from the receivers to the centralized/distributed processing utility(ies). To this end, the system 200 may be a centralized and/or distributed system.

FIG. 1C depicts functional modules/components that can be part of the system 200. The system 200 is connectable to, and optionally includes, signal receivers 210, including a plurality of receivers Rc₁-Rc_(n) capable of detecting an electro-magnetic signal S (e.g. radio-frequency (RF) signals) emitted from a signal source Src which is to be located. The signal receivers 210 generate respective signals/data S₁-S_(n) indicative of the emitted portion of the signal S respectively received thereby. The system 200 includes signal processing system 215 connectable to the receivers Rc₁-Rc_(n) for obtaining and processing the signals/data S₁-S_(n) received thereby during certain respective time intervals Δt₁-Δt_(n), and is configured and operable to process the signals/data S₁-S_(n) utilizing position data PD indicative of the positions R₁-R_(n) and/or indicative of the change in the positions of the receivers at the respective time intervals Δt₁-Δt_(n) and thereby estimate the location R_(Src) of the signal source Src.

It should be noted that herein and in the following, except where explicitly denoted otherwise, the subscript indices n, m denote the index of the receivers Rc₁-Rc_(n). Also, pairs of such subscript indices (e.g. m,n or mn) denote processing parameters/properties associated with the pair m,n of such receivers. Also it should be understood that notation of the curly brackets enclosing certain an element/parameter denoted with the sub-index (e.g. {Rc_(n)}) are used herein to indicate a group/collection of such elements/parameters (e.g. the notation may designate a group including several or all of the receivers Rc₁-Rc_(n)).

According to some embodiments, at least some of the plurality of receivers Rc₁-Rc_(n) are carried by separate/different vehicular platforms (e.g. terrestrial vehicles, and/or space vehicles, such as satellites, and/or airborne vehicles, and/or marine vehicles), and at least some of which are in motion during the operation of the system 200 for locating the signal source Src. To this end, the plurality of receivers Rc₁-Rc_(n) includes at least two receivers. According to some embodiments, three or more receivers are capable of detecting the signal S emitted from the signal source Src (which is to be located) can be used. This is however not mandatory.

The signal processing system 215 can include one or more processing unit(s) 230. As explained later in the specification, this processing unit 230 can perform various operations and processing of the signals that can be used for estimating the location of the signal source Src. According to some embodiments, one or more processing units 230 can be located at a central processing utility (located e.g. on the ground), and one or more processing units 230 can be located at other locations, such as at each receiver {Rc_(n)}, or on the platform on which each receiver {Rc_(n)} is located, or adjacent to each receiver {Rc_(n)}.

As indicated above, in certain implementations the signal processing system 215 is implemented as a distributed system. For example certain stages of the processing are applied to each of the signals {S_(n)} received by the receivers {Rc_(n)}, by utilizing suitable processing units of the processing system 215 located adjacent to the respective receivers {Rc_(n)} (e.g. at their vehicular platforms).

As will be readily appreciated by those versed in the art, there are various possible techniques for implementing the signal processing system 215. According to some embodiments, one or more components of the signal processing system 215 can be implemented by utilizing analogue signal processing means/circuits, and/or utilizing digital/computerized processing systems and/or by a combination of analogue and digital signal processing means/circuits. Components of the system which are implemented digitally may include or be associated with one or more digital processors, such as CPUs and/or DSPs for processing signals received, and with suitable samplers and/or analogue to digital converters (ADCs) for sampling the signals from the receivers and converting them to digital representation and/or possibly also with digital to analogue converters for converting digital signals to analogue forms in case the signals are processed by a combination of analogue and digital means.

As will be appreciated by those versed in the art, in case the system is implemented with analogue means, analogue circuits for implementing the operations described by method 100 may for example include a proper arrangement of signal amplifiers and signal frequency filters (e.g. band-pass filters) applying suitable amplification and/or filtering to the received signal to obtain desired frequency band thereof, signal mixers (e.g. homodyne/heterodyne) and possibly also local oscillators arranged to allow extraction of the phase of the signal, integrators and/or comparators configured and operable for generating signals indicative of the accumulated phase, and/or of the differential phase between the receivers. To this end, although the signal processing system 215 may be implemented by analogue means, in some embodiments it may be implemented in a more versatile manner by utilizing digital processing techniques.

For instance, in certain specific embodiments of the present invention, the receivers {Rc_(n)}, which may comprise for example antenna(s), generate an analogue signal corresponding to the signal {S_(n)}, respectively received thereby from the signal source Src. The receivers {Rc_(n)} can be associated with respective ADCs 235 converting analogue signals from the receivers into digital representations {S_(n)}, which are then fed to the signal processing system 215.

The process of locating the signal source Src can involve processing together of certain properties of the signals from at least two of the receivers {Rc_(n)}. To this end, the vehicular platforms carrying the receivers, or some of them, may also carry respective data communication modules 250 ₁, . . . , 250 _(n) (such as, but not limited to, antenna(s), etc.) for communicating data indicative of certain properties of the signals {S_(n)} to the signal processing system 215. The latter may also include a data communication module 260 (such as, but not limited to, antenna(s), etc.) for receiving the communicated data.

According to some embodiments, the signal processing system 215 also includes, or is in communication with, receivers' positioning module 240 operable to provide position data PD indicative of positions of the receivers {Rc_(n)} during respective time intervals {Δt_(n)}. For each receiver Rc_(n), the position data PD may indicate its position (such as 2D or 3D position, noted “R_(n)”) at two time points within respective time interval Δt_(n) (which lasts from t_(n) ^(init) to t_(n) ^(fin)).

For example, position data PD can include R_(n)(t_(n) ^(init)) and R_(n)(t_(n) ^(fin)). In other examples, PD can include at least a first/initial and second/final time points within the time interval Δt_(n).

Alternatively, or equivalently, position data PD may be indicative of the position R_(n) of the receiver Rc_(n) at one of the time points (e.g. R_(n)(t_(n) ^(init)) or R_(n)(t_(n) ^(fin))) and the change in that position ΔR_(n) during the time interval Δt_(n) between t_(n) ^(init) and t_(n) ^(fin).

As indicated above and shown in FIG. 1B, receivers Rc₁-Rc_(n), or at least some of them, are carried and moved by vehicular platforms (not specifically shown) along respective paths PTH₁-PTH_(n), which may be for example curved and/or straight paths. To this end, the receivers' positioning module 240 may include and/or be in communication with any suitable positioning system(s), such as GPS systems installed on the vehicular platforms and/or radar system tracking the vehicular platforms upon which the receivers {Rc_(n)} are installed, which can monitor the positions and/or motions of the respective vehicular platforms.

In this regard, as will be appreciated by those versed in the art, the receivers' positioning module 240 can include data communication capable of communication with positioning and/or tracking systems that are capable of tracking/monitoring/obtaining the positions of the receivers {Rc_(n)} (there are various known in the art types of such positioning/tracking systems which can be used in the present invention to obtain positions of the signal receivers). As indicated above, according to some embodiments, some of the receivers {Rc_(n)}, although not all of them, may be stationary (not moving) receivers. In this case, the static predetermined positions of the stationary receivers may be stored in a local and/or remote non-transitory memory and can be retrieved by the receivers' positioning module 240 directly and/or via the data communication. Further details on an embodiment of a method of estimating the location (noted e_(Src)) of the signal source Src will now be described with reference to method 100 of FIG. 1A and to the schematic illustration on FIG. 1B. Certain of the modules of system 200 may be configured and operable to perform the respective method operations.

In operation 105 of method 100, at least two signal receivers {Rc_(n)} capable of detecting a signal S emitted from the signal source Src that should be located, are provided. The receivers {Rc_(n)} are mounted on respective moving platforms, which carry them along respective paths (curved or straight paths) PTH₁-PTH_(n).

In FIG. 1B, three receivers Rc₁, Rc_(m) and Rc_(n) are explicitly depicted and shown for example to be respectively moving along: curved path PTH₁ in the general radial direction to the signal source Src, curved path PTH_(n) in an arbitrary general direction with respect to the signal source Src, and straight path PTH_(n) in the radial direction to the signal source Src.

The signal S emitted from the source Src during the movement of the receivers is illustrated schematically in FIG. 1B by the concentric circles depicting the equi-potential lines of the waveform of the signal S at a certain instant. The specific portions S₁, S_(m) and S_(n) of the signal S received by the receivers Rc₁, Rc_(m) and Rc_(n) during their movement along the paths PTH₁, PTH_(m) and PTH_(n) are also illustrated schematically.

Signal S comprises one or more sections. As a consequence, each signal {S_(n)} received by each receiver {Rc_(n)} comprises one or more of these sections. These sections can include certain modulation patterns applied to the carrier wave of the signal. According to some embodiments, the signal S may be modulated by modulation patterns formed according to various techniques, such as Amplitude Modulation (AM), Frequency Modulation (FM) (e.g. regular FM or linear FM) or any other modulation technique (e.g. Phase Modulation).

FIG. 1B shows schematically several sections (“modulation patterns”) of each signal {S_(n)} received by each receiver {Rc_(n)}, referenced p₁ ^((n)), p₂ ^((n)), and p₃ ^((n)), etc.

Each section or modulation pattern can be generally noted as p_(j) ^((n)), or p_(j,i) ^((n)), wherein “j” is the number of the received modulation pattern, “(n)” refers to receiver Rc_(n) and “i” refers to the number of the dwell, as explained later in the specification.

In the following, these sections are generally considered in the form of pulses, but this is not mandatory.

Although signal S comprises various pulses which are detected by the receivers {Rc_(n)}, an ambiguity can arise from the fact that it is not necessarily known if the j^(th) pulse p_(j) ^((n)) received by receiver Rc_(n) corresponds to the i^(th) pulse p_(j) ^((m)) received by receiver Rc_(m) or to another pulse, such as the i^(th) pulse p_(i) ^((m)) received by receiver Rc_(m), with i≠j.

This ambiguity can result from the fact that signal S has a constant pulse repetition interval (PRI). As a consequence, signals {S_(n)} can also have a constant PRI, which may introduce an ambiguity in the identification of the pulses between the different receivers {Rc_(n)}.

In addition, this ambiguity can also result from the fact that the PRI of signal S is low, and thus that the PRF of signal S is high. For example, the PRF can be more than 100 KHz, or equal to this value, this value being not limitative.

In addition, this ambiguity can also result from the fact that the receivers {Rc_(n)} are far from each other relative to the source Src. This can be reflected by the following equation, for each couple of receivers Rc_(m), Rc_(n):

∥e _(Src) −R _(m) ∥−∥e _(Src) −R _(n) ∥>>PRI.c  Equation 1

In Equation 1, R_(m) and R_(n) are the respective positions of receivers Rc_(m) and Rc_(n), e_(Src) is the position of source Src, PRI is the pulse repetition interval of signal S, and c is the velocity of light.

As shown in FIG. 1A, method 100 can include operation 110 which includes providing data indicative of the signals ({S_(n)}), which are received (and possibly sampled) by at least two receivers.

This can comprise providing data indicative of the signals S_(m) and S_(n) which are received (and possibly sampled) by receivers Rc_(m) and Rc_(n) (generally referred to as {Rc_(n)}) during their movement along their respective paths (according to some embodiments, one of the receivers may also be stationary). The provided data of the signals S_(m) and S_(n) may include only the part of those signals received by those receivers {Rc_(n)} during respective time intervals {Δt_(n)} during which the receivers move in between respective first positions {R_(n) ^(init)} to second positions {R_(n) ^((fin))} along their respective paths {PTH_(n)}. For example, in FIG. 1B, the signals S₁, S_(m) and S_(n) are provided, while the respective receivers Rc₁, Rc_(m) and Rc_(n) move from their first positions R₁ ^((init))(t₁), R_(m) ^((init))(t_(m)), and R_(n) ^((init))(t_(n)) at initial times t₁, t_(m) and t_(n), to second positions R₁ ^((fin))(t₁+Δt), R_(m) ^((fin))(t_(m)+Δt) and R_(n) ^((fin))(t_(n)+Δt) at the final times t₁+Δt, t_(m)+Δt and t_(n)+Δt. Here the time intervals {Δt_(n)}, for which the signals S₁, S_(m) and S_(n) are provided, correspond to respectively {Δt_(n)=[t_(n), t_(n)+Δ_(t)]} (i.e. Δt₁=[t₁, t₁+Δt], Δt_(m)=[t_(m), t_(m)+Δt], and Δt_(n)=[t_(n), t_(n)+Δt]). According to some embodiments, method 100 can be operated to estimate the location of the signal source by processing the signals received from the different receivers {Rc_(n)} at different times {t_(n)} (e.g. it may be that t₁≠t_(m)≠t_(n)).

According to some embodiments, the signals {S_(n)}, which are processed to determine the location of the signal source Src, are signals that were received by the receivers at time intervals {Δt_(n)} of equal duration (the duration is indicated by Δt).

This can be useful for reducing certain ambiguities, which may arise when computing the accumulated phases {Δφ^(n)} of the signals {S_(n)} (e.g. during unwrapping/unfolding procedures described hereinafter).

The method 100 can further comprise applying a processing 130 to determine differential phase differences ΔΔφ^(m,n) (ΔΔφ^(m,n)=Δφ^(m)−Δφ^(n)) which represent a difference between accumulated phases, Δφ^(m) and Δφ^(n), of the signals S_(m) and S_(n), received by one or more pairs {m,n} of the receivers, Rc_(m) and Rc_(n) during time intervals {Δt_(m)}, {Δt_(n)}, respectively.

Accumulated phases Δφ^(m) and Δφ^(n) can be determined in operation 120, which comprises applying a processing to each signal {S_(n)} to determine the phase {Δφ^(n)} that is accumulated during its respective time interval Δt_(n). According to some embodiments, and as described in the embodiment of FIG. 4 (see Equation 23), ΔΔφ^(m,n) can be computed without calculating explicitly Δφ^(m) nd Δφ^(n), by computing the difference between:

-   -   the difference in phase between the last pulse received by         receiver Rc_(m) and the last pulse received by receiver Rc_(n),         and     -   the difference in phase between the first pulse received by         receiver Rc_(m) and the first pulse received by receiver Rc_(n).

As shown in FIG. 1B, during the reception of each signal S_(n), its respective receiver Rc_(n) may move from an initial position R_(n) ^((init))(t_(n)) at initial time t_(n), to final position R_(n) ^((fin))(t_(n)+Δt) at final time t_(n)+Δt within the time interval Δt_(n). The accumulated phase Δφ^(n) in the received signal during that time interval can therefore be attributed to:

-   -   (1) change in the phase of the signal during the time duration         (e.g. Δt) of the time interval Δt_(n); and     -   (2) the change in position R_(n) of the respective receiver         Rc_(n) in between first/initial and second/final times t_(n)         ^((init)) and t_(n) ^((fin)) in the time interval Δt_(n), and         more specifically the change Δd_(n) of its distance d_(n) from         the signal source Src during that time interval, as depicted in         the figure. More specifically the change Δd_(n) of the distance         d_(n) of the n^(th) receiver is given by:

Δd _(n) =d _(n)(t _(n) ^(fin))−d _(n)(t _(n) ^(init))=∥R _(n)(t _(n) ^(fin))−e _(Src)(t _(n) ^(fin))∥−∥R _(n)(t _(n) ^(init))−e _(Src)(t _(n) ^(init))∥  Equation 2

To this end the accumulated change Δφ^(n) in the phase of the signal S_(n) received during the time interval Δt_(n) by receiver Rc_(n) is given by:

Δφ^(n)=2πfΔt+2πΔd _(n)/λ  Equation 3

where f is the frequency (e.g. carrier frequency) of the signal S emitted from the signal source Src, Δt is the duration of the time interval Δt_(n), λ is the wavelength of the signal S given by λ=c/f (where c being the speed of light), and Δd_(n) is the change in the distance d_(n) of the n^(th) receiver from the source Src during the time interval as given by Equation 2.

By inverting Equation 3, the change in the distance Δd_(n) to the source Src can be expressed in terms of the accumulated phase Δφ^(n) as follows: Δd_(n)=(c/2πf)Δφ^(n)-c·Δt. By combining this with Equation 2 above, a relation between the accumulated phase Δφ^(n) and the positions R_(n) and e_(Src) of the receiver Rc_(n) and the signal source Src can be obtained as follows:

∥R _(n)(t _(n) ^(fin))−e _(Src)(t _(n) ^(fin))∥−∥R _(n)(t _(n) ^(init))−e _(Src)((t _(n) ^(init))∥=(c/2πf)Δφ^(n) −c·Δt  Equation 4

where the time interval Δt_(n) during which the phase is accumulated is given by:

Δt _(n)=[t _(n) ^(init) ,t _(n) ^(fin) n]=[t _(n) ^(init) ,t _(n) ^(init) +Δt]

It is noted that the location of the signal source Src cannot be generally resolved from Equation 4 directly, because of the large ambiguity which may be included in the value of the accumulated phase Δφ^(n). Further processing described hereinafter will help to reduce/cancel this ambiguity.

Operation 130 provides a determination of differential phase ΔΔφ^(m,n) between the accumulated phases, Δφ^(n) and Δφ^(m), of the signals, S_(m) and S_(n), received by at least this pair {m,n} of the receivers Rc_(m) and Rc_(n). According to some embodiments, these operations can be applied to a plurality of different pairs {m,n} of the receivers. As explained later in the specification, according to some embodiments, the differential phase ΔΔφ^(m,n) is computed for each dwell i, and is thus noted ΔΔφ_(i) ^(m,n).

For each pair {m,n} of receivers, the differential phase ΔΔφ^(m,n) can be determined as follows:

ΔΔφ_(p) ^(m,n)=Δφ^(m)−Δφ^(n)  Equation 5

And more specifically by substituting Equation 3 into Equation 5:

ΔΔφ^(m,n)=2π/λ(Δd _(m) −Δd _(n))+2πf·(|Δt _(m) |−|Δt _(n)|).  Equation 6

According to some embodiments, the time intervals Δt_(m) and Δt_(n) of each pair {m,n} of the receivers for which the differential phase is calculated are of equal durations, namely |Δt_(m)|=|Δt_(n)|=Δt.

Accordingly, the second term in Equation 6 is nullified and the following relation is obtained for each pair {m,n} of receivers for which the differential phase is computed in 130:

ΔΔφ^(m,n)=2π/λ(Δd _(m) −Δd _(n)).  Equation 7

Substituting Equation 2 into Equation 7, the differential phase ΔΔφ^(m,n) is obtained in terms of the positions of the pair {m,n} of receivers, Rc_(m) and Rc_(n), and the position of the source Src at initial and final times t_(m) ^(init) t_(m) ^(fin) and t_(n) ^(init), t_(n) ^(fin) in the respective time intervals, Δt_(m) and Δt_(n).

ΔΔφ^(m,n)=2π/λ[(∥R _(m)(t _(m) ^(fin))−e _(Src) ∥−∥R _(m)(t _(m) ^(init))−e _(Src)∥)−(∥R _(n)(t _(n) ^(fin))−e _(Src) ∥−∥R _(n)(t _(n) ^(init))−e _(Src)∥)],  Equation 8

-   -   wherein e_(Src) is the position of the source S_(rc).

The method 100 can include operation 140 in which position data PD are provided (e.g. obtained from positioning modules 240 which are associated with the receivers, and/or which are monitoring their respective positions). As indicated above, position data PD can include data indicative of position of each receiver Rc_(n) in at least two, initial and final, time points, t_(n) ^(init) and t_(n) ^(fin), within the respective time interval Δt_(n) of the receiver; namely providing R_(n)(t_(n) ^(init)) and R_(n)(t_(n) ^(fin)). This is equivalently indicative of the position R_(n) of the receiver Rc_(n) at one of the time points (e.g. R_(n)(t_(n) ^(init))) and the change in that position ΔR_(n) during the time interval Δt_(n).

In view of the above, the only remaining unknown variable left in Equation 8 is related to the location of the signal source: e_(Src).

In operation 150, a processing can be applied to determine a first estimate ê_(Src) of the location of the signal source based on the differential phase ΔΔφ^(m,n) obtained for at least one pair {m,n} of the receivers in operation 130.

This can be achieved by solving Equation 8 (also called “ddphase” equation) above for at least one pair {m,n} of the receivers {Rc_(n)} while utilizing the positions {R_(n)} of the receivers {Rc_(n)} at their respective time intervals as obtained in operation 140 and also utilizing the differential phases ΔΔφ^(m,n) for different pairs of receivers obtained in operation 130.

As explained later in the specification, in some embodiments, the method is applied to a plurality of dwells (which corresponds to a period of time comprising a plurality of modulation patterns), and thus, if N dwells are present, N equations (N times Equation 8, one for each dwell) can be solved.

It should be noted that according to some embodiments, signal source Src is assumed and/or is known to be stationary. In this case, the velocity V_(Src) of the signal source needs not to be determined and/or it is assumed zero V_(Src)=0. In such cases the only unknown variable that needs to be determined by the set of Equation 8 is the stationary vector location of the signal source Src.

According to some embodiments, in operation 150 a set of at least V linearly independent equations similar to Equation 8 obtained for at least V independent pairs {m,n} of the receivers {Rc_(n)} are processed/computed and solved to determine the location e_(Src), of the signal source Src.

The first estimation of the source location can be provided with an accuracy area (also called accuracy ellipse, this shape being not limitative) which is the 2D or 3D area (around the estimated position ê_(Src)) in which it is assessed that the signal source can be located, based on the results of the “ddphase” equation (operation 150).

The accuracy area can be computed using mathematical tools, which can rely notably on the position data of the receivers, the estimated position of the signal source, and given standard deviations of the errors of parameters/measurements present in the equations.

For example, a covariance matrix of the errors of the parameters/measurements present in the equations can be computed, and the accuracy area can be computed based on this covariance matrix and the estimated position of the signal source. These parameters include e.g. position data of the receivers, velocity data of the receivers, the time of arrival of the modulation patterns of the signals, the phase measurements, and if applicable a first estimation of the altitude of the signal source (in some cases a digital model of the terrain “DTM” can be used to assess the altitude of the signal source).

A non-limitative example of a method of computing an accuracy ellipse is provided in Statistical Theory of Passive Location Systems, Don J. Torrieri, 1984, which is incorporated herein by reference. It is to be understood that other methods can be used for computing the accuracy area, using any appropriate mathematical tools.

A non-limitative example is illustrated in FIG. 1D, in which an accuracy ellipse 290 is drawn around the estimated location e_(Src).

The method 100 can further comprise operation 160 comprising determining data representative of difference in times of arrival Δt^(m,n) of the signals S_(m), S_(n) received by one or more pairs {m,n} of receivers. More particularly, these data can be representative of difference in times of arrival of sections (“modulation patterns”) of the signals S_(m), S_(n). Specific embodiments for performing operation 160 will be described with reference to FIGS. 2 and 3.

Difference in times of arrival of modulation pattern p_(j) ^((m)), received at receiver Rc_(m), and modulation pattern p_(j) ^((n)), received at receiver Rc_(n) (noted Δ_(pj) ^(m,n)), depends on the difference (divided by the speed of light c) between:

-   -   the distance between the source Src and the first receiver         Rc_(m), and     -   the distance between the source Src and the second receiver         Rc_(n).

This can be expressed, for a modulation pattern p_(j), by the general equation:

Δt _(p) _(j) ^(m,n)=(1/c)[∥R _(m)(TOA_(pj) ^((m)) −e _(Src) ∥−∥R _(n)(TOA_(pj) ^((n)))−e _(Src)∥],  Equation 9

wherein TOA_(pj) ^((m)) is the time of arrival of modulation pattern p_(j) ^((m)) at receiver Rc_(m) and TOA_(pj) ^((n)) is the time of arrival of modulation pattern p_(j) ^((n)) at receiver Rc_(n).

As explained later in the specification, this equation can be applied for each of a plurality of dwells.

According to some embodiments, a value representative of the difference in time of arrival of the modulation patterns can be computed over a given period of time (noted Δt ^(m,n) or over a dwell (noted Δt _(i) ^(m,n), for dwell i). This value can be e.g. an average of the value Δt _(p) ^(m,n) for all pulses p_(j) within this given period of time or within this dwell.

As already mentioned above, an ambiguity is present in data Δt_(p) _(j) ^(m,n) (and equivalently in Δt ^(m,n) and Δt _(i) ^(m,n)) due in particular to the fact that it is not known in advance if the j^(th) modulation pattern p_(j) ^((n)) received by receiver Rc_(n) corresponds to the j^(th) modulation pattern p_(j) ^((m)) received by receiver Rc_(m) or to another modulation pattern, such as the i^(th) modulation pattern p_(i) ^((m)) received by receiver Rc_(m), with i≠j.

This ambiguity is generally expressed as a multiple of the PRI of signal S, that is to say:

ambiguity=PRI.A,  Equation 10

-   -   wherein A is an unknown constant integer.

According to some embodiments, and as explained later in the specification, the signals S, S_(n), S_(m) can be divided into a plurality of dwells (a dwell is generally defined as a portion of a signal comprising a plurality of modulation patterns, such as pulses). If N dwells are present, the ambiguity can be defined for each dwell as follows:

ambiguity_(dwell i) =PRI.A _(i),  Equation 11

-   -   for i from 1 to N, and wherein A_(i) is an unknown constant         integer for each dwell.

The method 100 can further comprise operation 170 comprising using at least data representative of difference in times of arrival of the modulation patterns of the signals, differential phase differences ΔΔφ^(m,n), and the accuracy area to obtain one or more second estimates ê_(Src) ^(k) of the source location, wherein at least some of the second estimates of the source location, or all of these second estimates, are selected to be located within the accuracy area.

Operation 170 can rely in particular on at least one of the first estimates of the source location and the accuracy area obtained through the ddphase equations to limit the possible values of the ambiguity (multiple of the PRI) present in the difference in times of arrival of the modulation patterns of the signals. These possible values of the ambiguity can e.g. be bound within a limited set of values.

Operation 170 can comprise using the first estimate of the source location obtained through the ddphase equations to obtain an estimate of the difference in times of arrival of the modulation patterns of the signals through the DTOA equations. This estimate, together with differential phase differences ΔΔφ^(m,n) and the limited set of values of the ambiguity, can be used together to provide second estimates of the source location.

In particular, operation 170 can comprise solving a set of equations (herein after SETEQU) comprising both, for at least a pair of receiver Rc_(m), Rc_(n):

-   -   equations relating differential phase differences ΔΔφ^(m,n)         (between the accumulated phases at each receiver) to the         position of the receivers and the position of the source         location (such as Equation 8, also called ddphase equations);     -   equations relating the difference in times of arrival Δt^(m,n)         of the modulation patterns of the signals to the position of the         source and the position of the receivers (such as Equation 9,         also called DTOA equations).

According to some embodiments, SETEQU is solved for each of a plurality of dwells.

Operation 170 can in particular comprise solving this set of equations for a limited set of values of the ambiguity present in the data representative of difference in times of arrival, such as this limited set of values of the ambiguity provides second estimates of the source location which remain within the accuracy area.

According to some embodiments, in operation 170, the first estimate ê_(Src) of the source location (obtained using the ddphase equations) can be used in the DTOA equations to provide a first estimate Δ{circumflex over (t)}^(m,n) of data representative of difference in times of arrival of the modulation patterns of the signals.

According to some embodiments, in operation 170, SETEQU can be solved for all values of the difference in times of arrival of the modulation patterns of the signals which differ from Δ{circumflex over (t)}^(m,n) by an ambiguity which is within the limited set of values (this limited set of values can be calculated using the accuracy area, as explained hereinafter). The first estimate Δ{circumflex over (t)}^(m,n) generally comprises an error.

According to some embodiments, this error can be limited by comparing the first estimate Δ{circumflex over (t)}^(m,n) to data representative of difference in times of arrival of the modulation patterns of the signals S_(m), S_(n) received by a corresponding pair {m,n} of receivers, which were computed at operation 160 (e.g. Δ{circumflex over (t)}^(m,n)), and selecting an ambiguity which limits the corresponding difference.

In any case, the first estimate Δ{circumflex over (t)}^(m,n) still comprises an error due to the presence of an ambiguity.

Operation 170 can comprise selecting a limited set of values for the ambiguity present in the first estimate Δ{circumflex over (t)}^(m,n), based on the accuracy area (this limited set of values of the ambiguity constraints the solutions of SETEQU to be located within the accuracy area), and solving SETEQU for at least some or all possible values of the ambiguity of Δ{circumflex over (t)}^(m,n) which are present in this limited set of values. Mathematical tools such as “the maximal likelihood algorithm” can be used to solve SETEQU. This is however not limitative.

In particular, the selection of the limited set of values for the ambiguity present in the data representative of the difference of time of arrivals of the modulation pattern can rely on the fact that the multiple possible solutions to SETEQU are all separated by a distance c. PRI, and thus, knowing one or more dimensions of the accuracy area, the limited set of values for the ambiguity can be selected.

For example, assume the limited set of values is written k, wherein k is the range of integers belonging to [k_(min);k_(max)], and wherein the ambiguity in the data representative of difference in times of arrival of the modulation patterns of the signals is written k.PRI.

Operation 170 can thus comprise solving SETEQU for all values of Δ{circumflex over (t)}^(m,n)+k.PRI, with k belonging to [k_(min);k_(max)].

As mentioned, this can provide one or more second estimates of the source position, noted ê_(Src) ^(k), with k belonging to [k_(min);k_(max)].

A non-limitative example is provided in FIG. 1E, in which a plurality of second estimates ê_(Src) ^(k) of the source location are provided, all located within the accuracy area.

According to some embodiments, for each value of k, SETEQU is solved to provide second estimates ê_(Src) ^(k). As mentioned, algorithms such as the maximal likelihood algorithm can be used. This is however not limitative.

ê_(Src) ^(k) can be viewed as the intersection between N hyperboloids (corresponding to surfaces representing the geometric location of the solutions of the DTOA equations, for the N dwells) and N iso-ddphase surfaces (corresponding to surfaces representing the geometric location of the solutions of the ddphase equations, for the N dwells).

In some embodiments, a digital terrain model is used and it is assumed that the source is located on the surface of this terrain. Thus, ê_(Src) ^(k) can be found as the intersection between the N hyperboloids, the N iso-ddphase surfaces and the digital terrain model. This is however not limitative.

Operation 170 can comprise performing an optimization process to find one or more optimal values k′_(opt) among the range [k_(min);k_(max)], which are associated with corresponding ê_(Src) ^(k′) ^(opt) which are solutions of the ddphase and difference in times of arrival equations.

According to some embodiments, this optimization process can comprise performing an optimization of a function representative of an error of a solution to the equations based on the data representative of difference in times of arrival of the signals (DTOA equations of SETEQU) and/or of an error of a solution of the equations based on the differential phase differences (ddphase equations of SETEQU).

This optimization process can comprise e.g. minimizing an error of a solution to these equations.

This optimization process thus yields at least one optimal value k′_(opt), and thus at least one associated estimate of the source position ê_(Src) ^(k′) ^(opt) .

In some embodiments, this optimization process can be performed using the maximal likelihood algorithm mentioned above. This is however not limitative.

Over time, the volume of received data (data representative of the differential phase differences and of the difference in times of arrival) becomes larger, and thus the solution to the equations becomes more precise. Thus, after some convergence time, a single refined estimate ê_(Src) ^(k′) ^(opt) can be obtained.

Attention is now drawn to FIG. 2, which represents a possible embodiment of a method of performing operation 160.

As shown in FIG. 2, the method can comprise operation 164, which comprises processing the received signal S_(n) and recording the times of arrival of specific portion(s) of the signal S_(n) at the receivers Rc_(n). In other words, this operation 164 can comprise determining the receipt timings of modulated portions/sections of the received signals {S_(n)}.

In this connection, it should be understood that in case the signal S from the signal source is a signal which includes one or more modulation patterns (e.g. pulses) p_(j) ^((n)), indexed j, then the time of arrivals (TOAs) TOA_(pj) ^((n)) of the arrival of a modulation pattern (e.g. pulse) p_(j) ^((n)) (indexed j) at each receiver {Rc_(n)} may be recorded. Thus, the first pulse received by receiver Rc_(n) is p₁ ^((n)), the second pulse received by receiver Rc_(n) is p₂ ^((n)), etc.

In particular, the corresponding signals {S_(n)} respectively obtained by the receivers {Rc_(n)} can be processed (e.g. sampled and analyzed) to identify at least one modulation-pattern/pulse p_(j) ^((n)) therein (such identification can be performed by e.g. cross-correlation with signals received by other receivers and/or by identifying predetermined modulation patterns, such as the rise/fall time of a pulse—this is however not limitative).

Then, the times of arrival (TOAs) TOA_(pj) ^((n)) of the at least one pulse/modulation pattern p₁ ^((n)) at two or more of the receivers {Rc_(n)} are recorded. These data can be sent from each receiver to a central processing utility.

In case the signal source emits a modulated CW signal S (i.e. not pulsed), the TOAs {TOA_(p1) ^((n)) . . . TOA_(pK) ^((n))} of the signal S to the n different receivers {Rc_(n)} may be determined by e.g. cross correlating the signals {S₁ . . . S_(n)} received by different receivers to determine/measure the relative time difference between their reception times.

Operation 164 can be performed by a central processing utility or e.g. by one or more processing units included/located at/near the receivers Rc₁-Rc_(n) and adapted to process the signals S₁-S_(n) respectively received thereby to identify their profile (rise and/or fall times) and thereby determine the times of arrival of the different pulses by the different receivers,

According to some embodiments, sync data indicative of time synchronization of the receivers may be obtained and used to process and synchronize the times of arrival obtained by the receivers {Rc_(n)}. The sync data may be data indicative of time differences/lags between the clocks of the different receivers and a certain reference clock. The sync data may be obtained by any suitable known in the art time sync technique. Accordingly, the times of arrival may be synced by adding thereto the corresponding time lag. This is however not mandatory.

The method can further comprise operation 166, in which the differential time of arrival (DTOA) Δt_(p) _(j) ^(m,n) between the times of arrival of at least one pulse P₁ to the one or more pairs {m,n} of the receivers is determined/computed. The DTOA may be computed in operation 166 (e.g. by a processing unit of the central processing utility, or by a processing unit associated to a receiver if the receiver communicates TOA data with other receivers) as follows:

Δt ^(p) _(j) ^(m,n) =t _(p) _(j) ^(m) −t _(p) _(j) ^(n)  Equation 12

The DTOA can be calculated for all pulses received within a given period of time, such as within each dwell among a plurality of dwells.

It has already been mentioned that the modulation pattern p_(j) ^((m)) received at receiver Rc_(m) from the source Src and the modulation pattern p_(j) ^((n)) received at receiver RC, from the source Src do not necessarily correspond to the same modulation pattern of the signal S, due to the presence of an ambiguity, which can be expressed e.g. as multiple of the PRI of signal S.

According to some embodiments, the method can comprise operation 167, in which data representative of the DTOA can be calculated over a particular period of time, such as over a dwell.

For example, the average DTOA, or other statistical data representative of the DTOA over a period of time (such as median, etc.), such as over a dwell, can be computed. The following computation can be performed (the example of a dwell is taken, but this is not limitative):

Δ t ^(m,n)=mean_(pj∈dwell i)(TOA_(pj) ^((m))−TOA_(pj) ^((n))),  Equation 13

-   -   wherein “i” is the number of the dwell (e.g. there are N         dwells).

Since an ambiguity is present, Δt _(t) ^(m,n) comprises an ambiguity and thus we get (using Equation 11):

Δt _(i) ^(m,n) =Δt _(i) ^(m,n) +PRI.A _(i),

for each dwell i, wherein Δt_(i) ^(m,n) corresponds to all possible values of data representative of the DTOA of the modulation patterns that can be computed over a dwell i (these possible values depend on the unknown value of the ambiguity).

Attention is now drawn to FIG. 3 which describes possible embodiments of a method of performing operations 150 to 170. These embodiments are exemplary and not limitative.

As already mentioned with respect to FIG. 1A, operation 150 can comprise determining a first estimate of the location of the signal source based on the differential phase ΔΔφ^(m,n) between the accumulated phases, Δφ^(m) and Δφ^(n), of the one or more pairs {m,n} of receivers and their respective positions.

According to some embodiments, differential phase differences ΔΔφ^(m,n) between accumulated phases can be calculated over one or more periods of time, also called dwells. Assume there are N dwells, wherein each dwell is indexed by integer “i”. Thus, differential phase differences between accumulated phases can be obtained for each dwell, and can be written ΔΔφ_(i) ^(m,n).

Operation 350 (which can be part e.g., of operation 150) can comprise solving, for at least one dwell, or for at least two dwells, the following equation (which is equivalent to Equation 8 cited above, but expressed for each dwell):

$\begin{matrix} {{\Delta\Delta\varphi}_{i}^{m,n} = {\frac{2\pi\; f}{c}\left\lbrack {\left( {{{e_{Src} - {R_{m}\left( t_{{p\; 1},i}^{(m)} \right)}}} - {{e_{Src} - {R_{n}\left( t_{{p\; 1},i}^{(n)} \right)}}}} \right) - \left( {{{e_{Src} - {R_{m}\left( t_{{pK},i}^{(m)} \right)}}} - {{e_{SRC} - {R_{n}\left( t_{{pK},i}^{(n)} \right)}}}} \right)} \right.}} & {{Equation}\mspace{14mu} 15} \end{matrix}$

In Equation 15, p_(j,i) ^((n)) the i^(th) pulse received within dwell i by receiver Rc_(n).

In addition, t_(pj,i) ^((n)) can be defined as follows. Every modulation pattern or pulse p_(j,i) ^((n)) dwell i, which is received by a receiver Rc_(n) at time TOA_(pj) ^((n)) is active between time TOA_(pj,i) ^((n)) and TOA_(pj,i) ^((n))+ε, wherein ε is the duration of the modulation pattern or of the pulse. Time t_(pj,i) ^((n)) is a particular time which is chosen between TOA_(pj,n) ^((n)) and TOA_(pj,n) ^((n))+ε, generally as a multiple of the time clock step. This choice is a matter of definition and other definitions can be used.

Equation 15 reflects the fact that a differential phase difference ΔΔφ_(i) ^(m,n) of the modulation patterns received at a pair of the receivers Rc_(m) and Rc_(n), is indicative of a distance difference between the changes in the distances of the respective receivers Rc_(n) and Rc_(n) from the signal source during the time interval of the dwell.

By solving Equation 15 for one or more dwells, a first estimate ê_(S) _(rc) of the source location can be obtained. In addition, for a given “e” which is solution of Equation 15 (such as e=ê_(Src)) an error ε_(ΔΔφ) _(i) _(m,n) (e) is present. According to some embodiments, statistical data representative of this error can be computed, such as the standard deviation σ_(ΔΔφ) _(i) _(m,n) (e).

As already mentioned above (see operation 150), an accuracy area, around the estimated position ê_(Src), is also obtained.

In operation 360 (which can be part e.g. of operation 160), difference in times of arrival of modulation patterns of the signals (Δ{circumflex over (t)}_(i) ^(m,n)) within each dwell can be estimated using the first estimate ê_(Src).

In other words, the first estimate ê_(S) _(rc) of the source location can be injected in the DTOA equations in order to find a first estimate Δ{circumflex over (t)}_(i) ^(m,n) of the difference in times of arrival of the signals within each dwell (in particular of the average DTOA over all pulses within a dwell).

In addition, as already mentioned above, the difference in times of arrival of the modulation patterns of the signals comprises an ambiguity. Thus, the estimate Δt_(i) ^(m,n) comprises an error due to the ambiguity, which can be limited by using the value of the difference in times of arrival of modulation patterns of the signals that was computed in operation 167.

The following equations can be solved, for each dwell i:

$\begin{matrix} {{{\Delta\;{\hat{t}}_{i}^{m,n}} = {{\frac{1}{c}\left( {{{{\hat{e}}_{S_{rc}} - {R_{m}\left( \overset{\_}{t} \right)}}} - {{{\hat{e}}_{S_{rc}} - {R_{n}\left( \overset{\_}{t} \right)}}}} \right)} + {error}}}{{{error}} \leq \frac{PRI}{2}}{{\Delta\;{\hat{t}}_{i}^{m,n}} = {{\Delta\;{\overset{\_}{t}}_{i}^{m,n}} + {{PRI}.{\hat{A}}_{i}^{m,n}}}}{{wherein}\mspace{14mu}{\hat{A}}_{i}^{m,n}\mspace{14mu}{is}\mspace{14mu} a\mspace{14mu}{suitable}\mspace{14mu}{{integer}.}}} & {{Equation}\mspace{14mu} 16} \end{matrix}$

In Equation 16, ê_(Src), R_(m)(t), R_(n)(t), PRI, c, Δt_(i) ^(m,n), are the known inputs. Equation 16 is solved to find Â_(i) ^(m,n) and therefore the value Δ{circumflex over (t)}_(i) ^(m,n), for each dwell i.

In this equation, t is the time at the center of the dwell. This choice is a matter of definition and other times in the dwell can be used.

At the output of operation 360, we thus obtain an estimate Δ{circumflex over (t)}_(i) ^(m,n) of the difference of times of arrival of the modulation patterns within each dwell (which is e.g. representative of an average of this value within each dwell).

As shown in FIG. 1E, a solution to both the DTOA equations and ddphase equations based on ΔΔφ_(i) ^(m,n) and Δ{circumflex over (t)}_(i) ^(m,n) is the value ê_(Src) ⁰ (which is the closest value to ê_(Src) obtained based only on the ddphase equations).

ê_(Src) ⁰, which is associated to Δ{circumflex over (t)}_(i) ^(m,n), provides only an estimate of the real location of the source since the ambiguity related to the PRI is still present.

As illustrated in FIG. 1E, Δ{circumflex over (t)}_(i) ^(m,n)+k.PRI can also be used in the DTOA equations to estimate the source location, wherein k is to be determined.

In some embodiments, the value of k can be approximated as independent from the dwells. This approximation is particularly relevant over time, when the volume of data increases, since the accuracy area becomes narrower.

Operation 370 (which can be part e.g. of operation 170) can comprise selecting a set of limited values for the multiple of the PRI for which the solutions to the DTOA equations (and to the ddphase equations) are (all of them, or at least some of them) within the accuracy ellipse.

As shown in FIG. 1E, the accuracy ellipse, whose center is generally located near ê_(Src) ⁰, can be used to limit the possible values of k. Indeed, all possible solutions to the DTOA equations and to the ddphase equations are separated by a distance which is a multiple of PRI.c.

In particular, if we assume that L is the length along the long axis of the accuracy ellipse (this can apply to any accuracy area which is not an ellipse, by selecting the long axis of the accuracy area), k can be selected between K₁ and K₂, wherein:

$K_{1} = {{\frac{\frac{- L}{2}}{{PRI}.c}\mspace{14mu}{and}\mspace{14mu} K_{2}} = \frac{\frac{+ L}{2}}{{PRI}.c}}$

Once a limited set of values has been obtained for k, the DTOA equations and the ddphase equations can be solved to find other possible estimate ê_(Src) ^(k) for the source location.

For all dwells i (i from 1 to N), and for k between K₁ and K₂, the following equations can be solved (equivalent to SETEQU mentioned above, but this time for each of a plurality of dwells, thus noted SETEQU_(i)):

$\begin{matrix} {{\Delta\Delta\varphi}_{i}^{m,n} = {\frac{2\pi\; f}{c}\left\lbrack {{\left( {{{{\hat{e}}_{S_{rc}}^{k} - {R_{m}\left( t_{{p\; 1},i}^{(m)} \right)}}} - {{{\hat{e}}_{S_{rc}}^{k} - {R_{n}\left( t_{{p\; 1},i}^{(n)} \right)}}}} \right) - \left( {{{{\hat{e}}_{S_{rc}}^{k} - {R_{m}\left( t_{{pK},i}^{(m)} \right)}}} - {{{\hat{e}}_{S_{rc}}^{k} - {R_{n}\left( t_{{pK},i}^{(n)} \right)}}}} \right) + {{{ɛ_{\Delta\Delta\varphi}}_{i}^{m,n}\left( {\hat{e}}_{S_{rc}}^{k} \right)}\left( {{ddphase}\mspace{14mu}{equations}} \right)\Delta\;{\hat{t}}_{i}^{m,n}} + {k.{PRI}}} = {{\frac{1}{c}\left( {{{{\hat{e}}_{S_{rc}}^{k} - {R_{m}\left( \overset{\_}{t} \right)}}} - {{{\hat{e}}_{S_{rc}}^{k} - {R_{n}\left( \overset{\_}{t} \right)}}}} \right)} + {{ɛ_{\Delta\; t_{i}^{m,n}}\left( {\hat{e}}_{S_{rc}}^{k} \right)}\left( {{DTOA}\mspace{14mu}{equations}} \right)}}} \right.}} & {{Equation}\mspace{14mu} 17} \end{matrix}$

In these equations, ε_(ΔΔφ) _(i) ^(m,n) is the error of the ddphase equations and ε_(Δt) _(i) ^(m,n) is the error of the DTOA equations.

A plurality of possible estimate ê_(Src) ^(k) is obtained, one for each value of k. This can be seen in FIG. 1E.

Operation 380 (which can be part of operation 170) can comprise selecting one or more values for k, and thus of corresponding estimates ê_(Src) ^(k), which meet an optimization criterion. This can comprise minimizing a function representative of:

-   -   an error of a solution to the equations based on the data         representative of difference in times of arrival of the signals         (DTOA equations of SETEQU_(i)), and/or     -   an error of a solution to the equations based on the         differential phase differences (ddphase equations of         SETEQU_(i)).

In particular, according to some embodiments, the following optimization criterion can be used. For each integer k between K₁ and K₂, we define:

$\begin{matrix} {{{Likelihood}\mspace{11mu}(k)} = {{\sum\limits_{i = 1}^{N}\left( \frac{ɛ_{\Delta\; t_{i}^{m,n}}\left( {\hat{e}}_{S_{rc}}^{k} \right)}{\sigma_{\Delta\; t_{i}^{m,n}}\left( {\hat{e}}_{S_{rc}}^{k} \right)} \right)^{2}} + {\sum\limits_{i = 1}^{N}\left( \frac{ɛ_{{\Delta\Delta}\;\varphi_{i}^{m,n}}\left( {\hat{e}}_{S_{rc}}^{k} \right)}{\sigma_{{\Delta\Delta\varphi}_{i}^{m,n}}\left( {\hat{e}}_{S_{rc}}^{k} \right)} \right)^{2}}}} & {{Equation}\mspace{14mu} 18} \end{matrix}$

Let {circumflex over (k)} be the integer that brings to minimum the likelihood function. Then ê_(Src) ^({circumflex over (k)}) can be selected as the best estimate of the location of the source. According to some embodiments, a plurality of values {circumflex over (k)} can be obtained, for example which provides a value of the likelihood function which is close to the minimum. Thus, other possible solutions ê_(Src) ^({circumflex over (k)}) can be obtained.

According to some embodiments, over time, when the number of dwells N increases, a sharper minimum of the likelihood function can be obtained, thus yielding to a unique solution {circumflex over (k)} and to a unique estimate ê_(Src) ^({circumflex over (k)}) of the source location.

According to some embodiments, when new data are received, operations 130-170 can be applied again to a larger set of data comprising both the old data and the newly received data, in order to refine the estimate of the source location.

According to some embodiments, the one or more estimates of the source location obtained based on the old data can be used together with the newly received data in order to refine the estimate of the source location. This can be used in particular when the ambiguity present in the signals received by the receivers has been cancelled or reduced using the old data.

The method can comprise repeating operations 164, 166 and 167 using the new data. In addition, operation 360 can be repeated. In operation 360, a first estimate of the source location is needed. The estimate of the source location obtained based on the old data can be used as this first estimate.

Then, a new estimate of the source location can be computed using the new DTOA and ddphase equations, the estimate of the source location obtained based on the old data, and an old covariance matrix of the errors of the estimation of the location of the source (which can be calculated based on the old DTOA and ddphase equations and the covariance matrix of the errors of the parameters/measurements).

Operations 370 and 380 need not to be repeated, since the ambiguity has been cancelled or reduced based on the old data.

Attention is now drawn to FIG. 4, which describes possible embodiments of a method of computing ΔΔφ_(i) ^(m,n).

The method can comprise synchronizing the time slots of the pulses between the pair(s) of receivers. This is however not mandatory and is described as a possible example only.

As mentioned above, every modulation pattern or pulse p_(j,i) ^((m)) of dwell i, which is received by a receiver Rc_(m) at time TOA_(pj,i) ^((m)), is active between time TOA_(pj,i) ^((m)) and TOA_(pj,i) ^((m))+ε, wherein ε is the duration of the modulation pattern or of the pulse. Time t_(pj,i) ^((m)), also called “time slot”, is a particular time which is chosen between TOA_(pj,i) ^((m)) and TOA_(pj,i) ^((m))+ε, generally as a multiple of the time clock step.

In order to synchronize the time slots between the receivers Rc_(m) and Rc_(n) within a dwell i (or within a given duration), the method can comprise operation 400 comprising calculating the difference in time between the time slot t_(p1,i) ^((m)) of the first pulse p_(1,i) received by receiver Rc_(m) within dwell i and the time slot t_(p1,i) ^((n)) of the first pulse p_(1,i) received by receiver Rc_(m) within dwell i.

The following computation can be performed:

Δτ=t _(p1,i) ^((m)) −t _(p1,i) ^((n))  Equation 19

Then, the value of Δτ can be added to the time slots of the other pulses received by receiver Rc_(m), in order to obtain adjusted time slots.

The following computation can be performed:

{circumflex over (t)} _(pj,i) ^((m)) =t _(pj,i) ^((n))+Δτ  Equation 20

In this equation, {circumflex over (t)}_(pj,i) ^((m)) is the adjusted time slot of pulse p_(j,i) ^((m)) received by receiver Rc_(m) within dwell i.

The value of the phase φ_(pj,i) ^((m)) of the signal received by each receiver Rc_(m) at each time slot t_(pj,i) ^((m)) can be measured e.g. by a processing unit located at each receiver.

Operation 410 can comprise extrapolating the phase at each adjusted time slot {circumflex over (t)}_(pj,i) ^((m)).

The following computation can be performed:

$\begin{matrix} {{\hat{\varphi}}_{{pj},i}^{(m)} = {\varphi_{{pj},i}^{(m)} + {\left( {{\hat{t}}_{{pj},i}^{(m)} - t_{{pj},i}^{(m)}} \right) \cdot \frac{d\;\varphi_{{pj},i}^{(m)}}{dt}}}} & {{Equation}\mspace{14mu} 21} \end{matrix}$

Operation 420 can comprise calculating differential phase differences between the modulation patterns received at the pair of receivers (differential phase differences between the first modulation pattern received at the pair of receivers, between the second modulation pattern, etc.). The differential phase differences can be calculated at the adjusted time slots.

The following computation can be performed:

Δφ_(pj,i) ^(m,n)={circumflex over (φ)}_(pj,i) ^((m))−φ_(pj,i) ^((n))  Equation 22

Operation 430 can comprise unwrapping the values of Δφ_(pj,i) ^(m,n). This comprises e.g. adding iteratively to the phase Δφ_(pj,i) ^(m,n) a multiple of 2·π so that the absolute value of the phase difference of each two consecutive values of Δφ_(pj,i) ^(m,n) is less than π.

According to some embodiments, the phases {circumflex over (φ)}_(pj,i) ^((m)) and φ_(pj,i) ^((n)) are first unwrapped. This comprises e.g. adding iteratively to the phase {circumflex over (φ)}_(pj,i) ^((m)) and φ_(pj,i) ^((n)) a multiple of 2·π so that the absolute value of the phase difference of each two consecutive pulses is less than π Then, after this unwrapping operation, Δφ_(pj,i) ^(m,n) is computed.

Possible embodiments for unwrapping the phases of the pulses or of the accumulated phase over a given time interval will be described with reference to FIGS. 7A and 7B.

The value Δφ_(pj,i) ^(m,n) has an ambiguity which is a multiple of 2·π.

Operation 440 can comprise determining the differential phase ΔΔφ_(i) ^(m,n) between the accumulated phases, for a given dwell i, which may be computed according to Equation 23.

ΔΔφ_(i) ^(m,n)=Δφ_(pK,i) ^(m,n)−Δφ_(p1,i) ^(m,n)  Equation 23

In Equation 23, p_(K,i) is the last pulse of dwell i and p_(1,i) is the first pulse of dwell i.

Another possibility to compute ΔΔφ_(i) ^(m,n) is to calculate Δφ_(i) ^(m) which is the accumulated phase of receiver Rc_(m) within dwell i (Δφ_(i) ^(m)={circumflex over (φ)}_(pK,i) ^((m))−{circumflex over (φ)}_(p1,i) ^((m))), and to calculate Δφ_(i) ^(n) which is the accumulated phase of receiver Rc_(n) within dwell i (Δφ_(i) ^(n)=φ_(pK,i) ^((n))−φ_(p1,i) ^((n))), and then to compute ΔΔφ_(i) ^(m,n)=Δφ_(i) ^(m)−Δφ_(i) ^(n).

The differential phase ΔΔφ_(i) ^(m,n) of a dwell comprises an ambiguity, which is a multiple of 2·π. This is due in particular to the fact that Δφ_(pj,i) ^(m,n) comprises such an ambiguity.

Operations 400 and 410 can be performed at each receiver, or at the central processing utility. Operations 420 to 440 are generally performed at the central processing utility (or at a receiver if data pertaining to the phase values are exchanged between the receivers).

Attention is drawn to FIGS. 5 and 6 which describe possible methods of reducing the ambiguity present in the accumulated phases and/or in the differential phase differences between the accumulated phases.

As shown in FIG. 5, a first method can comprise operation 500 which comprises using a bound value which bounds the value of the difference between Δφ_(pj,i) ^(m,n) for two consecutive modulation patterns/pulses (that is to say that bounds Δφ_(p) _(j+1,i) ^(m,n)−Δφ_(p) _(j,i) ^(m,n)).

The following computation can be performed:

$\begin{matrix} {{{{{\Delta\varphi}_{{{pj} + 1},i}^{m,n} - {\Delta\varphi}_{{pj},i}^{m,n}}} \leq {\frac{2\pi\; f}{c}{\left( {v_{m} + v_{n}} \right) \cdot {pri}_{j}^{n}}}},{{{wherein}\mspace{14mu} v_{m}} = {\frac{{dR}_{n}}{dt}}},{v_{n} = {\frac{{dR}_{n}}{dt}}},{{{and}\mspace{14mu}{pri}_{j,i}^{n}} = {t_{{{pj} + 1},i}^{(n)} - t_{{pj},i}^{(n)}}}} & {{Equation}\mspace{14mu} 24} \end{matrix}$

This limits the possible number of values for Δφ_(pj,i) ^(m,n) and thus reduces the ambiguity.

Attention is drawn to FIG. 6 which illustrates a second method of limiting the ambiguity (which can be performed in addition to the first method of FIG. 5, or alternatively to the first method of FIG. 5).

This second method can rely on a rough estimation obtained using the DTOA technique. Operation 600 can comprise in particular utilizing the differential times of arrival Δt_(p) _(j) ^(m,n), Δt_(p) _(i) ^(m,n) of two or more pulses p_(j) and p_(i) to reduce the ambiguity which can be present in ΔΔφ_(i) ^(m,n).

This is based on the understanding that the differential phase ΔΔφ^(m,n), which is indicative of a difference Δd_(n)−Δd_(m) between the changes Δd_(n) and Δd_(m) in the distances, d_(n) and d_(m), of the respective receivers Rc_(m) and Rc_(n) from the signal source Src during the time interval Δt, corresponds to the difference Δt_(p) _(j) ^(m,n)−Δt_(i) ^(m,n) between the differential times of arrival Δt_(p) _(j) ^(m,n), Δt_(p) _(i) ^(m,n) of two pulses p_(j) and p_(i) (which respectively occur at the beginning and the end of a time interval Δt′) to the receivers Rc_(n) and Rc_(m). More specifically, the differential phase ΔΔφ^(m,n) (ddphase) over the time interval Δt should be proportional to the differential times of arrival of the pulses p_(j) and p_(i) occurring at the beginning and end of the pulses in the dwell within the time interval Δt′. More specifically, the differential phase ΔΔφ^(m,n) should satisfy the following relation:

$\begin{matrix} {\frac{{\Delta\Delta\varphi}_{i}^{m,n}}{\Delta\; t^{i}} \approx \frac{{\Delta\Delta\varphi}_{j}^{m,n}}{\Delta\; t^{j}} \approx {2\pi\; f\frac{{\Delta\; t_{p_{j}}^{m,n}} - {\Delta\; t_{p_{i}}^{m,n}}}{\Delta\; t^{\prime}}}} & {{Equation}\mspace{14mu} 25} \end{matrix}$

where f represents the frequency of the signal S.

In many cases, the differential phase and the differential times of arrival is measured/computed for one or more dwells of pulses. In this case, Equation 25 above may be represented as follows

$\begin{matrix} {\frac{{\Delta\Delta\varphi}_{i}^{m,n}}{\Delta\; t^{i}} \approx \frac{{\Delta\Delta\varphi}_{j}^{m,n}}{\Delta\; t^{j}} \approx {2\pi\; f\frac{{\Delta\; t_{p_{j}}^{m,n}} - {\Delta\; t_{p_{i}}^{m,n}}}{\Delta\; t^{\prime}}}} & {{Equation}\mspace{14mu} 26} \end{matrix}$

where ΔΔφ_(i) ^(m,n) is the measured differential phase over the time interval Δt^(i) of the first dwell i, ΔΔφ_(j) ^(m,n) is the measured differential phase over the time interval Δt^(j) of the second dwell j and Δt′ is the difference between the time at the center of dwell i and the time at the center of dwell j.

Thus, the expression of Equation 26 above can be used to set-bounds-to/estimate the possible values that the differential phase ΔΔφ_(i) ^(m,n) can acquire for each dwell i. Accordingly, in some embodiments of the present invention, operation 600 is incorporated/included in 130, in which the relation of Equation 26 is used to disambiguate the differential phase ΔΔφ^(m,n) or ΔΔφ_(i) ^(m,n) calculated in 130.

This may be achieved for example by modifying the differential phase ΔΔφ^(m,n), expressed in Equation 8 above, to read as follows:

ΔΔφ^(m,n)=2π/λ(Δd _(m) −Δd _(n))+2πZ  Equation 27

where Z is an integer number that is selected such that the differential phase ΔΔφ^(m,n) (or ΔΔφ_(i) ^(m,n) for a dwell) is within the boundaries given by the errors in the DTOA measurements set by Equation 26.

In the above example the DTOA positioning technique provides for resolving possible ambiguities in the differential phase ΔΔφ^(m,n). Alternatively, or additionally, information of other positioning techniques (e.g. from the differential Doppler technique) may also be used for resolving this ambiguity in the differential phase ΔΔφ^(m,n).

Reference is now made together to FIGS. 7A and 7B illustrating possible embodiments of methods of determining the phases and unwrapping the phases of pulses received at each receiver.

Assume a signal S_(n) is received at receiver Rc_(n). This signal comprises two of more pulses p₁ ^((n)) and p₂ ^((n)).

In operation 700S, each modulation pattern/pulse received in a certain time interval Δt can be sampled/divided into a plurality of samples corresponding to time intervals TS₁-TS_(L) of durations shorter than half the period T (being one over the frequency f) of the carrier wave of the signal. In FIG. 7B, the time slots t_(p1) ^((n)), t_(p2) ^((n)) (which are located within each pulse, and were defined in reference to FIG. 4), are also illustrated.

Then in operation 700F portions/samples {TS_(L)} of the pulse corresponding to the time intervals can be transformed into the frequency domain (e.g. via Fourier transform) and their respective phases {φ_(L)} modulus 2π can be determined. The phases are therefore bounded within a range of 2π (e.g. in the range [0, 2π] or [−π, π]). The phases {φ_(L)} modulus 2π of the signal portions (samples) {TS_(L)} obtained in that way are illustrated by the blackened points in FIG. 7B.

Operation 700P can include unfolding (unwrapping) the phases {φ_(L)}, to unwrap the modular representation of the phases such that each phase φ_(L) will present the actual phase of the signal S_(n) accumulated from the beginning of the pulse until the time of the respective time interval TS_(L). The unwrapped phases are illustrated by the hollow circles in FIG. 7B.

Operation 700P may be carried out by various techniques. For example in some cases sub operations (i) to (iii) are carried out as described in the following:

-   -   700P.(i) process the phases {φ_(L)} to identify abrupt reduction         in the phase φ_(k+1) of a successive time interval TS_(k+1) with         respect to a signal phase φ_(k) of a time interval TS_(k)         preceding it. To this end, abrupt reduction may be considered a         decrease (or increase) of more than π in the phase value whose         magnitude is larger than the level of noise associated with the         receiver.     -   700P.(ii) upon identification of such abrupt reduction, adding         multiples of 2π to the phase φ_(k+1) for the successive time         TS_(k+1) and also to all the phases φ_(k+2)−φ_(L) of the time         intervals succeeding it for this pulse; and     -   700P.(iii) carrying out 700P.(i) and 700P.(ii) for each pair of         successive time intervals of this pulse.

Operation 700 can be performed for each pulse separately.

According to some embodiments, if the phases are required only on specific time points, such as at the time slots, the phases can be unwrapped only at these time slots, instead of unwrapping the phases at each time interval of each pulse. Operation 700 can be applied similarly to these specific time points.

This provides for unwrapping the phases {φ_(L)} and obtaining the unwrapped phase profiles PP1 and PP2 of the signal S_(n), as illustrated in the dashed line in FIG. 7B.

The signal sections may be, for example, pulses of duration in the order of microseconds (e.g. 1 μSec) which are transmitted with pulse repetition interval (PRI) in the order of microseconds (e.g. 10 μSec). Accordingly, the time separation between the pulses may be in the order of the PRI.

As indicated above, the operation 700 may be implemented near/at each/some of the receivers and/or at the central processing utility, depending on the implementation of system 200.

The purpose of operation 710 is to obtain data indicative of the phase profile PP_(n) of the signal S_(n) during the entire time interval Δt, from which the accumulated phase Δφ^(n) during the time interval Δt can be determined/estimated. In 710 the phase profile PP_(n) for the entire time interval Δt is obtained by fitting the phase profile PP1 and PP2 onto a common line. As indicated above, this may be performed at the central processing utility. For example, the phase profile PP1 of the first pulse/modulated-section p₁ ^((n)) the received signal S_(n) is used to construct the guideline GD illustrated in the figure FIG. 7B. The phase profile PP2 of the second pulse/modulated-section p₂ ^((n)) of the received signal S_(n) is fitted/matched to the guideline GD by adding thereto a certain phase value Dθ, which is an integral multiple of 2π, selected in accordance with the time separation SEP between the pulses, which may be for example estimated from the derivative of the phase profile(s) PP1 and/or PP2. The fitted phase profile PP2 is illustrated in the figure and is indicated by PP2′. Accordingly, the phase profile PP_(n) for the entire time interval Δt is estimated.

In operation 720 the phase profile PP_(n) is used to determine the accumulated phase Δφ^(n) that is accumulated during the time interval Δt (Δφ^(n) can be calculated by computing the difference between the phases of first and last points of the phase profile PP_(n)).

It should be however noted that in cases where operation 720 is conducted, some ambiguity might be introduced in the thus determined accumulated phase Δφ^(n). This is because the added phase value Dθ which is used to match and fit the phase profile(s) may be ambiguous and may actually supplement 2πk value to the accumulated phase where k is any integer value (positive, negative, or zero). The ambiguity can be reduced by using e.g. the method of FIG. 5.

The ambiguity in the accumulated phase Δφ^(n) is manifested in an ambiguity in the differential phase ΔΔφ^(m,n), which is computed e.g. in operation 130 of method 100. The ambiguity can be reduced by using e.g. the method of FIG. 6.

The method of FIGS. 7A and 7B was described in the context of the unwrapping of phases φ_(p) _(j) ^(n) of pulses of a signal S_(n) received at receiver Rc_(n), in order to obtain differential phases Δφ^(n) over a given time interval (such as a dwell).

This method can be applied similarly to the unwrapping of differential phases differences Δφ_(p) _(j) ^(m,n) (or Δφ_(pj,i) ^(m,n)) of each pulse. In particular, the differential phase differences between the receivers are first computed for each pulse, based on the wrapped phases of the pulses of signal Sn (see Equation 22), and then an unwrapping in compliance with the method of FIGS. 7A and 7B can be performed on the values Δφ_(p) _(j) ^(m,n) (or Δφ_(pj,i) ^(m,n)) over a given interval, such as a dwell. Accordingly, ΔΔφ^(m,n) (or ΔΔφ_(i) ^(m,n)) can be computed after this unwrapping, by computing the difference between the differential phase differences of the last pulse and the differential phase differences of the first pulse over the time interval (see e.g. Equation 23).

It is to be noted that the various features described in the various embodiments may be combined according to all possible technical combinations.

It is to be understood that the invention is not limited in its application to the details set forth in the description contained herein or illustrated in the drawings. The invention is capable of other embodiments and of being practiced and carried out in various ways. Hence, it is to be understood that the phraseology and terminology employed herein are for the purpose of description and should not be regarded as limiting. As such, those skilled in the art will appreciate that the conception upon which this disclosure is based may readily be utilized as a basis for designing other structures, methods, and systems for carrying out the several purposes of the presently disclosed subject matter.

Those skilled in the art will readily appreciate that various modifications and changes can be applied to the embodiments of the invention as hereinbefore described without departing from its scope, defined in and by the appended claims. 

1. A system for estimating a physical location of a signal source emitting a signal S, the system comprising a processor and memory circuitry configured to: obtain measured data indicative of a signal S_(n) informative of the signal S and received from the signal source by each of a number of at least two receivers {Rc_(n)} during time intervals {Δt_(n)}, where n is an index indicating the n^(th) receiver Rc_(n), obtain position data indicative of positions {R_(n)} of said at least two receivers during said time intervals {Δt_(n)} respectively; apply a processing to determine differential phase differences ΔΔφ^(m,n) which represent a difference between accumulated phases, Δφ^(m) and Δφ^(n), of the signals, S_(m) and S_(n), received by at least one pair {m,n} of the receivers, Rc_(m) and Rc_(n) during time intervals {Δt_(n)}, {Δt_(m)}, respectively, apply a processing to determine a first estimate of the physical location of said signal source based on said position data and said differential phase differences {ΔΔφ^(m,n)} of said at least one pair {m,n} of receivers, said first estimate being associated with an accuracy area, apply a processing to determine data representative of difference in times of arrival of modulation patterns of the signals S_(m), S_(n) received by said at least one pair {m,n} of receivers, and for said at least one pair {m,n} of receivers, use at least said data representative of difference in times of arrival of the modulation patterns of the signals, said differential phase differences ΔΔφ^(m,n), and said accuracy area to determine one or more second estimates ê_(Src) ^(k) of the physical location of the signal source, wherein at least some of these one or more second estimates ê_(Src) ^(k) of the physical location of the signal source are located within the accuracy area, use the one or more second estimates ê_(Src) ^(k) to estimate the physical location of the signal source, thereby enabling estimating said physical location of the signal source using said data representative of difference in times of arrival of modulation patterns comprising an ambiguity caused by at least a constant pulse repetition interval (PRI) of the signal S and a difference between a distance from a receiver Rc_(n) to the signal source and a distance from a receiver Rc_(m) to the signal source which is larger than a threshold.
 2. The system of claim 1, configured to: use at least said accuracy area to obtain a limited set of values for said ambiguity.
 3. The system of claim 2, configured to: for one or more values of said limited set of values for said ambiguity, determine said one or more second estimates ê_(Src) ^(k) of the physical location of the signal source based on a relationship relating differential phase differences ΔΔφ^(m,n) to the position data of said at least one pair {m,n} of receivers and to the physical location of the signal source, and a relationship relating said difference in times of arrival of modulation patterns of the signals S_(m), S_(n) to the position data of said at least one pair {m,n} of receivers and to the physical location of the signal source, for one or more values of the ambiguity within said limited set.
 4. The system of claim 2, configured to: use the first estimate of the physical location of the signal source to obtain an estimate of the difference in times of arrival of the modulation patterns of the signals, and use said estimate of the difference in times of arrival of the modulation patterns of the signals, said limited set of values of said ambiguity and said differential phase differences ΔΔφ^(m,n) to determine said one or more second estimates ê_(Src) ^(k) of the physical location of the signal source.
 5. The system of claim 1, configured to: use the first estimate ê_(Src) ^(k) of the physical location of the signal source to determine Δ{circumflex over (t)}^(m,n), wherein Δ{circumflex over (t)}^(m,n) is an estimate of data representative of difference in times of arrival of the modulation patterns of the signals.
 6. The system of claim 5, configured to: determine said one or more second estimates ê_(S) _(rc) of the physical location of the signal source based on a relationship relating said differential phase differences ΔΔφ^(m,n) to the position data of the receivers and to the physical location of the signal source, and a relationship relating said estimate of the data representative of difference in times of arrival of the modulation patterns Δ{circumflex over (t)}^(m,n) plus a model k.PRI of said ambiguity to the position data of the receivers and to the physical location of the signal source, wherein k is an integer selected such that said one or more second estimates ê_(Src) ^(k) are within said accuracy area and wherein PRI is a pulse repetition interval of the signal S.
 7. The system of claim 1, configured to: obtain a set of limited values for said ambiguity, said obtaining comprising selecting a plurality of multiples of a pulse repetition interval of the signal S, for which associated data representative of difference in times of arrival of modulation patterns of the signals provide an estimate of the physical location of the signal source which is within the accuracy area.
 8. The system of claim 1, configured to: select an optimized set of values of said ambiguity according to an optimization criterion, said optimization criterion being representative of at least one of: an error of a solution to equations relating differential phase differences ΔΔφ^(m,n) to the position data of the receivers and to the physical location of the signal source, and an error of a solution to equations relating difference in times of arrival of modulation patterns of the signals S_(m), S_(n) to the position data of the receivers and to the physical location of the signal source, and provide said one or more second estimates ê_(Src) ^(k) of the physical location of the signal source based on said optimized set of values.
 9. The system of claim 1, in which conditions (i) and (ii) are met: (i) the signal S has a constant pulse repetition interval (PRI), and (ii) |∥e−s_(m)∥−∥e−s_(n)∥|>PRI.c, wherein c is the speed of light, e is the physical location of the signal source, s_(m), is the position of the receiver Rc_(m) and s_(n) is the position of the receiver Rc_(n).
 10. The system of claim 1, wherein the signal S has a pulse repetition frequency (PRF) which is higher or equal to 100 KHz, wherein PRF=1/PRI in which PRI is the pulse repetition interval of the signal S.
 11. The system of claim 1, configured to obtain measured data indicative of a signal S_(n) informative of the signal S and received from the signal source by each of a number of at least two receivers {Rc_(n)} during a time interval Δt_(i) of a dwell i, obtain position data indicative of positions {R_(n)} of said at least two receivers during said time interval Δt_(i); apply a processing to determine differential phase differences ΔΔφ_(i) ^(m,n) which represents a difference between accumulated phases, Δφ_(i) ^(m) and Δφ_(i) ^(n), of the signals, S_(m) and S_(n), received by at least one pair {m,n} of the receivers, Rc_(m) and Rc_(n) during time interval Δt_(i), apply a processing to determine a first estimate of the physical location of said signal source based on position data and said differential phase differences ΔΔφ_(i) ^(m,n) of said at least one pair {m,n} of receivers, said first estimate being associated with an accuracy area, apply a processing to determine data representative of difference in times of arrival of modulation patterns of the signals S_(m), S_(n) received by said at least one pair {m,n} of receivers within said dwell, wherein said data comprise an ambiguity, for said at least one pair {m,n} of receivers, and for a plurality of said dwells, using at least said data representative of difference in times of arrival of the modulation patterns of the signals, said differential phase differences ΔΔφ_(i) ^(m,n), and said accuracy area to determine one or more second estimates ê_(Src) ^(k) of the physical location of the signal source, wherein at least some of these one or more second estimates ê_(Src) ^(k) of the physical location of the signal source are located within the accuracy area.
 12. The system of claim 11, wherein each signal S_(n) comprises a plurality of modulation patterns p_(j,i) ^((n)) within dwell i, and j an index representing the j^(th) modulation pattern, wherein said determining of ΔΔφ_(i) ^(m,n) comprises computing Δφ_(p,j,i) ^(m,n) which is representative of the phase difference between the phase of modulation pattern p_(j,i) ^((n)) received at receiver Rc_(n) and the phase of modulation pattern p_(j,i) ^((m)) received at receiver Rc_(m), wherein the system is configured to use a bound value which bounds the value of the difference between Δφ_(pj,i) ^(m,n) for two consecutive modulation patterns, to limit a phase ambiguity present in Δφ_(pj,i) ^(m,n).
 13. The system of claim 1, wherein: a dimension of the accuracy area has a length L, said ambiguity is modelled as k.PRI, with PRI the pulse repetition interval of signal S, and k is selected within a range which is between K1 and K2, wherein: $K_{1} = {{\frac{\frac{- L}{2}}{{PRIC}.c}\mspace{14mu}{and}\mspace{14mu} K_{2}} = \frac{\frac{+ L}{2}}{{PRI}.c}}$
 14. A method of estimating a physical location of a signal source emitting a signal S, the method comprising, by a processor and memory circuitry: obtaining measured data indicative of a signal S_(n) informative of the signal S and received from the signal source by each of a number of at least two receivers {Rc_(n)} during time intervals {Δt_(n)}, where n is an index indicating the n^(th) receiver Rc_(n), obtaining position data indicative of positions {R_(n)} of said at least two receivers during said time intervals {Δt_(n)} respectively; applying a processing to determine differential phase differences ΔΔφ^(m,n) which represent a difference between accumulated phases, Δφ^(m) and Δφ^(n), of the signals, S_(m) and S_(n), received by at least one pair {m,n} of the receivers, Rc_(m) and Rc_(n) during time intervals {Δt_(n)}, {Δt_(m)}, respectively, applying a processing to determine a first estimate of the physical location of said signal source based on said position data and said differential phase differences {ΔΔφ^(m,n)} of said at least one pair {m,n} of receivers, said first estimate being associated with an accuracy area, applying a processing to determine data representative of difference in times of arrival of modulation patterns of the signals S_(m), S_(n) received by said at least one pair {m,n} of receivers, and for said at least one pair {m,n} of receivers, using at least said data representative of difference in times of arrival of the modulation patterns of the signals, said differential phase differences ΔΔφ^(m,n), and said accuracy area, to determine one or more second estimates ê_(Src) ^(k) of the physical location of the signal source, wherein at least some of these one or more second estimates ê_(Src) ^(k) of the physical location of the signal source are located within the accuracy area, using the one or more second estimates ê_(Src) ^(k) to estimate the physical location of the signal source, thereby enabling estimating said physical location of the signal source using said data representative of difference in times of arrival of modulation patterns comprising an ambiguity caused by at least a constant pulse repetition interval (PRI) of the signal S and a difference between a distance from a receiver Rc_(n) to the signal source and a distance from a receiver Rc_(m) to the signal source which is larger than a threshold.
 15. The method of claim 14, comprising, by the processor and memory circuitry: using at least said accuracy area to obtain a limited set of values for said ambiguity.
 16. The method of claim 15, comprising, by the processor and memory circuitry: for one or more values of said limited set of values for said ambiguity, determine said one or more second estimates ê_(Src) ^(k) of the physical location of the signal source based on a relationship relating differential phase differences ΔΔφ^(m,n) to the position data of said at least one pair {m,n} of receivers and to the physical location of the signal source, and a relationship relating said difference in times of arrival of modulation patterns of the signals S_(m), S_(n) to the position data of said at least one pair {m,n} of receivers and to the physical location of the signal source, for one or more values of the ambiguity within said limited set.
 17. The method of claim 14, comprising: using the first estimate of the physical location of the signal source to obtain an estimate of the difference in times of arrival of the modulation patterns of the signals, and using said estimate of the difference in times of arrival of the modulation patterns of the signals, said limited set of values of said ambiguity and said differential phase differences ΔΔφ^(m,n) to determine said one or more second estimates ê_(Src) ^(k) of the physical location of the signal source.
 18. The method of claim 14, comprising: using the first estimate ê_(S) _(rc) of the physical location of the source to determine Δ{circumflex over (t)}^(m,n), wherein Δ{circumflex over (t)}^(m,n) is an estimate of data representative of difference in times of arrival of the modulation patterns of the signals. determining said one or more second estimates ê_(S) _(rc) of the physical location of the signal source based on a relationship relating said differential phase differences ΔΔφ^(m,n) to the position data of the receivers and to the physical location of the signal source, and a relationship relating said estimate of the data representative of difference in times of arrival of the modulation patterns Δ{circumflex over (t)}^(m,n) plus a model k.PRI of said ambiguity to the position data of the receivers and to the physical location of the signal source, wherein k is an integer selected such that said one or more second estimates ê_(Src) ^(k) are within said accuracy area and wherein PRI is a pulse repetition interval of the signal S.
 19. The method of claim 15, in which at least one of conditions (i) and (ii) is met: (i) the signal S has a constant pulse repetition interval (PRI), and |∥e−s_(m)∥−∥e−s_(n)∥|>PRI.c, wherein c is the speed of light, e is the physical location of the signal source, s_(m) is the position of the receiver Rc_(m) and s_(n) is the position of the receiver Rc_(n), and (ii) S has a PRF which is higher or equal to 100 KHz.
 20. A non-transitory computer readable medium comprising instructions that, when executed by a processor and memory circuitry (PMC), cause the PMC to perform operations comprising estimating a physical location of a signal source, said estimating comprising: obtaining measured data indicative of a signal S_(n) informative of the signal S and received the signal source by each of a number of at least two receivers {Rc_(n)} during time intervals {Δt_(n)}, where n is an index indicating the n^(th) receiver Rc_(n), obtaining position data indicative of positions {R_(n)} of said at least two receivers during said time intervals {Δt_(n)} respectively; applying a processing to determine differential phase differences ΔΔφ^(m,n) which represents a difference between accumulated phases, Δφ^(m) and Δφ^(n), of the signals, S_(m) and S_(n), received by at least one pair {m,n} of the receivers, Rc_(m) and Rc_(n) during time intervals {Δt_(n)}, {Δt_(m)}, respectively, applying a processing to determine a first estimate of the physical location of said signal source based on said position data and said differential phase differences {ΔΔφ^(m,n)} of said at least one pair {m,n} of receivers, said first estimate being associated with an accuracy area, applying a processing to determine data representative of difference in times of arrival of modulation patterns of the signals S_(m), S_(n) received by said at least one pair {m,n} of receivers, and for said at least one pair {m,n} of receivers, using at least said data representative of difference in times of arrival of the modulation patterns of the signals, said differential phase differences ΔΔφ^(m,n), and said accuracy area to determine one or more second estimates ê_(Src) ^(k) of the physical location of the signal source, wherein at least some of these one or more second estimates ê_(Src) ^(k) of the physical location of the signal source are located within the accuracy area, using the one or more second estimates ê_(Src) ^(k) to estimate the physical location of the signal source, thereby enabling estimating said physical location of the signal source using said data representative of difference in times of arrival of modulation patterns comprising an ambiguity caused by at least a constant pulse repetition interval (PRI) of the signal S and a difference between a distance from a receiver Rc_(n) to the signal source and a distance from a receiver Rc_(m) to the signal source which is larger than a threshold. 